Lemma REF  and Theorem REF  allow us to create other statistical tests for the null hypothesis. For example, we can take the maximum norm instead of the \(L^2\) -norm of the vector \(\hat{\mathbb {C}}\)  or other vectors. For the classic ACF, this was done in [1]}. More generally, we can take the \(L^p\) -norm for \(p \in [1, \infty ]\) , with \(p = \infty \)  corresponding to the maximum norm.
